Stochastic averaging for stochastic differential equations driven by fractional Brownian motion and standard Brownian motion

Abstract

In this paper, an averaging principle for multidimensional, time dependent, stochastic differential equations (SDEs) driven by fractional Brownian motion and standard Brownian motion was established. We combined the pathwise approach with the Itô stochastic calculus to handle both types of integrals involved and proved that the original SDEs can be approximated by averaged SDEs in the manner of mean square convergence.